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Part BCSIR NET June 2025the-k-at-least-1-is-what-makes-these-strict-inequalities

The k at least 1 is what makes these strict inequalities

Let p, q be non-negative integers. Consider the following statements: (A) There is an integer k ≥ 1 such that p + k = q. (B) There is an integer k ≥ 1 such that q + k = p. Which of the following statements is true?

  1. A.There exist non-negative integers p, q such that both (A) and (B) are true.
  2. B.Both (A) and (B) are false if and only if p = q.✓
  3. C.For all non-negative integers p and q, (A) or (B) is true.
  4. D.There exists p ≠ q such that both (A) and (B) are false.

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests boundary and endpoint.

See pricing

50 are analysed free — try those first.

The trap it tests

Boundary and endpoint

The statement turns at the edge of the interval, the domain, or the parameter range.

Drill statements like this

More on this topic

The chapter behind this: Elements of set theory: operations, De Morgan and difference — free to read

From The Real Line › Elements of set theory: operations, De Morgan and difference

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